The steady state concentration of the activated molecule `[A**]` in the following sequence of steps is given by:
`A + A overset(k_(1))(rarr)A+A^(**)A^(**)+Aoverset(k_(2))(rarr)2A`

Options

A. `k_(2)[A]//k_(1)`
B. `k_(1)[A]//k_(2)`
C. `k_(1)k_(2)[A]`
D. `k_(1)k_(2)//[A]`

Answer

b

Explanation

`A+Aoverset(k_(1))(rarr)A+A^(**), A^(**)+Aoverset(K_(2))(rarr)2A`
Rate of decomposition `A=k_(1) [A]^(2)`
Rate of formation `A=k_(2)[A][A^(**)]`
At equilibrium, rate of decomposition = rate of formation
`k_(1)[A]^(2)=k_(2)[A][A^(**)]`
`[A^(**)]=k_(1)/k_(2)[A]`